Abstract
Let G = (V, E) be an undirected multi-graph where V and E are a set of nodes and a set of edges, respectively. Let k and l be fixed nonnegative integers. This paper considers location problems of finding a minimum size of node-subset S ⫅ V such that node-connectivity between S and x is greater than or equal to k and edge-connectivity between S and x is greater than or equal to l for every x ∈ V . This problem has important applications for multi-media network control and design. For a problem of considering only edge-connectivity, i.e., k = 0, an O(L(|V |, |E|, l)) = O( |E|+ |V |2 + |V |min {|E |; l |V |} min {l, |V |mponents for h = 1, 2,..., l. This paper presents an O(L(|V|, |E|, l)) time algorithm for 0≤ k ≤ 2 and l ≥ 0. It also shows that if k ≥ 3, the problem is NP-hard even for l = 0. Moreover, it shows that if the size of S is regarded as a parameter, the parameterized problem for k = 3 and l ≤ 1 is FPT (fixed parameter tractable).
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Ito, H., Ito, M., Itatsu, Y., Uehara, H., Yokoyama, M. (2000). Location Problems Based on Node-Connectivity and Edge-Connectivity between Nodes and Node-Subsets. In: Goos, G., Hartmanis, J., van Leeuwen, J., Lee, D.T., Teng, SH. (eds) Algorithms and Computation. ISAAC 2000. Lecture Notes in Computer Science, vol 1969. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-40996-3_29
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DOI: https://doi.org/10.1007/3-540-40996-3_29
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